Multi-Carrier and Spread Spectrum Systems: From OFDM and MC ...

Multi-Carrier Transmission 29serial data symbolsserialtoparallelconvertersub-carrier f 0sub-carrier f 1sub-carrier f Nc −1•parallel data symbolsT s = N c·T dFigure 1-4Multi-carrier modulation with N c = 4 sub-channelscomplexity of the equalizer. OFDM is a low complex technique used to modulate multiplesub-carriers efficiently by using digital signal processing [6, 15, 29, 51, 54].An example of multi-carrier modulation with four sub-channels N c = 4 is depicted inFigure 1-4. Note that the three-dimensional time/frequency/power density representationis used to illustrate the principle of various multi-carrier and multi-carrier spread spectrumsystems. A cuboid indicates the three-dimensional time/frequency/power density range ofthe signal, in which most of the signal energy is located and does not make any statementabout the pulse or spectrum shaping.An important design goal for a multi-carrier transmission scheme based on OFDM ina mobile radio channel is that the channel can be considered as time-invariant duringone OFDM symbol and that fading per sub-channel can be considered as flat. Thus, theOFDM symbol duration should be smaller than the coherence time (t) c of the channeland the sub-carrier bandwidth should be smaller than the coherence bandwidth (f ) c ofthe channel. By fulfilling these conditions, the realization of low complex receivers ispossible.1.2.1 Orthogonal Frequency Division Multiplexing (OFDM)A communication system with multi-carrier modulation transmits N c complex-valuedsource symbols 1 S n , n = 0,...,N c − 1, in parallel on to N c sub-carriers. The sourcesymbols may, for instance, be obtained after source and channel coding, interleaving, andsymbol mapping. The source symbol duration T d of the serial data symbols results afterserial-to-parallel conversion in the OFDM symbol durationT s = N c T d . (1.31)The principle of OFDM is to modulate the N c sub-streams on sub-carriers with a spacingofF s = 1 (1.32)T s1 Variables that can be interpreted as values in the frequency domain like the source symbols S n , each modulating another sub-carrierfrequency, are written with capital letters.